Using a Ball that Bounces Down a Flight of Stairs to Determine Energy Dissipation in Stepped Spillway with a Fully Developed Hydraulic Jump

Abstract

In this paper, the authors reviewed the characteristics of a ball that descended one step each bounce of a flight of stairs and drew an analogy with a stepped spillway with a fully developed hydraulic jump. They used this concept with equations of motion, classical hydraulic jump, and Chanson’s model for energy dissipation in the stepped spillway to formulate a mechanistic model for energy dissipation rates. The range of Froude numbers used was between 5 and 16. They used data from previous researchers’ publications on drop structures to verify the new model and data sets generated compared well with the measured data sets. Results showed that energy dissipation rates along the stepped spillway increased with the increasing number of steps but decreased with increasing discharges. It also showed the optimal number of steps for 100% energy dissipation.